Given equations are x- - y-z = 2, - x - 3 y - 2 z + 4, -x - 2 z = 10 .
It seems you have missed to write = in the 2nd equation so i have fixed the sign and going to solve the following system of equations:
x-y-z=2 ...(i)
-x-3y-2z=4 ...(ii)
-x-2z=10 ...(iii)
solve (i) for x
x=2+y+z ...(iv)
plug (iv) into (ii)
-x-3y-2z=4
-(2+y+z)-3y-2z=4
-2-y-z-3y-2z=4
-2-4y-3z=4
-4y-3z=6...(v)
plug (iv) into (iii)
-x-2z=10
-(2+y+z)-2z=10
-2-y-z-2z=10
-2-y-3z=10
-y=12+3z
y=-12-3z...(vi)
plug (vi) into (v)
-4y-3z=6
-4(-12-3z)-3z=6
48+12z-3z=6
48+9z=6
9z=-42
z=-14/3
Now plug value of z into (vi)
y=-12-3z=-12-3(-14/3)=-12+14=2
y=2
plug value of y and z into (iv)
x=2+y+z=2+2-14/3=-2/3
Hence final answer is x=-2/3, y=2, z=-14/3